A coin is tossed twice and outcomes are recorded. If the random variable X represents the number of heads in the experiment, then the expectation of X will be:

In class XII, suppose 5% of boys and 0.25% of girls are physically fit for a game. A fit student is selected at random from this class having same number of boys and girls. If the probability that the selected student is a girl is $\frac{m}{n}$, gcd(m, n) = 1, then m + n is equal to

Four cards are drawn successively without replacement from a deck of 52 playing cards. The probability that all the four cards are king is:

A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn, and then another ticket is drawn without replacing the first one. Then the probability that both the tickets show at least one even number, is

If X is a random variable and $a$, $b$ are real numbers, then which of the following statements are true?

(A) $Var(aX+b) = a^2 Var(X)$

(B) $E(aX+b)= a E(X) + b$

(C) $E(aX+b)= a E(X) - E(b)$

(D) $Var(aX+b)= a Var(X) + b$

Choose the correct answer from the options given below:

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be heart then the probability of the missing card to be a heart is:

If A and B are two events such that $A \neq \emptyset$, B $\neq \emptyset$, then which of following is/are TRUE:

A. $P(B/A)=P(A).P(B)$

B. $P(B/A)=\frac{P(A\cap B)}{P(A)}$

C. $P(A'/B')=\frac{1-P(A\cup B)}{1-P(B)}$

D. $P(B/A).P(A/B)=2$

Choose the correct answer from the options given below: